One minimize problem - numerical and symbolical solutions

[ValeryOchkov]

I am trieing to solve one minimize problem.

Numerical is OK - see please the picture and the Mathcad 15 sheet in attach.

But numerical - problems - see please two sheets (15 and Prime 3.1) in attach.

Any help please.

The problem of the race (from point 1 to point 4) on the lawn, plowing and asphalt
or

A a ray of light in a three-layer plate

[ValeryOchkov]

Ждем-с! I am waiting for the solution!

[ValeryOchkov]

A try in Maple

[AlvaroDíaz]

Hi Valery.

What Maple is telling is that the critical points are the set indicated as x2=x3 and x3=x4. This is one DOF. Thus the mininum for your problem isn't a point, it is a curve given by

This is, any point at this curve its a local extrema, and a minumun if t''(u)>0, which I don't check.

Best regards.

Alvaro.

[ValeryOchkov]

Maple solution:

[ValeryOchkov]

But I cannot get this solution in Mathcad - Mathcad 15 not answer with this task - see please the picture above 

[ValeryOchkov]

Maple-solution with units

[Fred_Kohlhepp]

[ValeryOchkov]

Thanks, Fred!

But no answer on my Mathcad Prime 3.1 - see please the picture and the attach

[Fred_Kohlhepp]

Interesting.

3.0 will solve it but 3.1 won't!

Wonder what the difference is.

[ValeryOchkov]

Fred Kohlhepp написал(а):

Interesting.

3.0 will solve it but 3.1 won't!

Wonder what the difference is.

Fred, attach, please, your Prime 3.0 sheet!

[Fred_Kohlhepp]

Attached

[ValeryOchkov]

Fred Kohlhepp написал(а):

Attached

Sorry, no solution in my Prime 3.1

[ValeryOchkov]

No answer

[ValeryOchkov]

I have the answer without a, b, c Prime 3.1 sheet in attach.

[Fred_Kohlhepp]

Found a typing error in the file.

Corrected and units added

[ValeryOchkov]

Thanks, Fred,

but I think by numerical solution the minimize function not find is more...

[AlvaroDíaz]

Well, Fred's Prime is more powerfull.

But I insist: there are a curve as solution, not only an isolated point.

Best regards.

Alvaro.

[ValeryOchkov]

Sorry, Alvaro!

Maple gives us a point as solution (3 roots - one real and 2 complex). See please the counter plot above too.

Or I do not understand some thing

[AlvaroDíaz]

Oh, yes, you're right. I see the plot not enough close. Solution is the intersection of this 3 surfaces:

Best regards.

Alvaro.

[ValeryOchkov]

It is one optic problem.

Video Link : 7197

[ValeryOchkov]

An optic solution of the problem

[ValeryOchkov]

With plots

[ValeryOchkov]

But no symbolical solution